ECE 2300 Circuit Analysis

1
ECE 2300 Circuit Analysis
Lecture Set 1 Voltage, Current, Energy and Power
Dr. Dave Shattuck Associate Professor, ECE Dept.
2
Module 1 Part 1What are Current and Voltage?
Modified from Dr. Dave Shattuck, Dynamic
Presentation of Key Concepts, modules for circuit
theory self-study.
3
Overview

• In this part, we will cover
• Definitions of current and voltage
• Hydraulic analogies to current and voltage
• Reference polarities and actual polarities

4
Current Formal Definition

• Current is the net flow of charges, per time,
  past an arbitrary plane in some kind of
  electrical device.
• We will only be concerned with the flow of
  positive charges. A negative charge moving to
  the right is conceptually the same as a positive
  charge moving to the left.
• Mathematically, current is expressed as

Charge, typically in Coulombs C
Current, typically in Amperes A
Time, typically in seconds s
5
The Ampere

• The unit of current is the Ampere, which is a
  flow of 1 Coulomb of charge per second, or
• 1A 1Coul/sec
• Remember that current is defined in terms of the
  flow of positive charges.

One coulomb of positive charges per second
flowing from left to right - is equivalent to
- one coulomb of negative charges per second
flowing from right to left.
6
What is the Deal with the Square Brackets and
?

• The unit of current is the Ampere, which is a
  flow of 1 Coulomb of charge per second, or
• 1A 1Coul/sec
• Remember that current is defined in terms of the
  flow of positive charges.

In these notes, we place units inside square
brackets ( and ). This is done to make it
clear that the units are indeed units, to try to
avoid confusion. This step is optional. Showing
units is important. Using the square brackets is
not important, and is not required.
7
Hydraulic Analogy for Current

• It is often useful to think in terms of hydraulic
  analogies.
• The analogy here is that current is analogous to
  the flow rate of water
• Charges going past a plane per time
• is analogous to
• volume of water going past a plane in a pipe per
  time.

8
Water flow Current

• So, if we put a plane (a screen, say) across a
  water pipe, and measure the volume of water that
  moves past that plane in a second, we get the
  flow rate.
• In a similar way, current is the number of
  positive charges moving past a plane in a
  current-carrying device (a wire, say) in a
  second.
• The number of charges per second passing the
  plane for each Ampere of current flow is called a
  Coulomb, which is about 6.24 x 1018 electron
  charges.

Animated graphic provided by David Warne, student
in UH ECE Dept.
9
Voltage Formal Definition

• When we move a charge in the presence of other
  charges, energy is transferred. Voltage is the
  change in potential energy as we move between two
  points it is a potential difference.
• Mathematically, this is expressed as

Energy, typically in Joules J
Voltage, typically in Volts V
Charge, typically in Coulombs C
10
What is a Volt?

• The unit of voltage is the Volt. A Volt is
  defined as a Joule per Coulomb.
• Remember that voltage is defined in terms of the
  energy gained or lost by the movement of positive
  charges.
• One Joule of energy is lost from an electric
  system when a Coulomb of positive charges moves
  from one potential to another potential that is
  one Volt lower.

11
Hydraulic Analogy for Voltage

• Hydraulic analogy voltage is analogous to
  height. In a gravitational field, the higher
  that water is, the more potential energy it has.
• The voltage between two points
• is analogous to
• the change in height between two points, in a
  pipe.

12
Hydraulic AnalogyVoltage and Current
height voltage
flow rate current
13
Hydraulic Analogy With Two Paths
Water is flowing through the pipes.
There is a height difference across these pipes.
We can extend this analogy to current through and
voltage across an electric device
14
Current Through

• If we have two pipes connecting two points, the
  flow rate through one pipe can be different from
  the flow rate through the other. The flow rate
  depends on the path.

15
Voltage Across

• No matter which path you follow, the height is
  the same across those two points. The height
  does not depend on the path

16
Polarities

• It is extremely important that we know the
  polarity, or the sign, of the voltages and
  currents we use. Which way is the current
  flowing? Where is the potential higher? To keep
  track of these things, two concepts are used
• Reference polarities, and
• Actual polarities.

17
Reference Polarities

• The reference polarity is a direction chosen for
  the purposes of keeping track. It is like
  picking North as your reference direction, and
  keeping track of your direction of travel by
  saying that you are moving in a direction of 135
  degrees. This only tells you where you are going
  with respect to north, your reference direction.

18
Actual Polarity

• The actual polarity is the direction something is
  actually going. We have only two possible
  directions for current and voltage.
• If the actual polarity is the same direction as
  the reference polarity, we use a positive sign
  for the value of that quantity.
• If the actual polarity is the opposite direction
  from the reference polarity, we use a negative
  sign for the value of that quantity.

19
Relationship between Reference Polarity and
Actual Polarity

• The actual polarity is the direction something is
  actually going. The reference polarity is a
  direction chosen for the purposes of keeping
  track. We have only two possible directions for
  current and voltage.
• Thus, if we have a reference polarity defined,
  and we know the sign of the value of that
  quantity, we can get the actual polarity.
• Example Suppose we pick our reference direction
  as up. The distance we go up is 5feet.
  We know then, that we have moved an actual
  distance of 5feet down.

20
Reference Polarities

• Reference polarities do not indicate actual
  polarities. They cannot be assigned incorrectly.
  You cant make a mistake assigning a reference
  polarity to a variable.
• Always assign reference polarities for the
  voltages and currents that you name. Without
  this step, these variables remain undefined. All
  variables must be defined if they are used in an
  expression.

21
Polarities for Currents

• For current, the reference polarity is given by
  an arrow.
• The actual polarity is indicated by a value that
  is associated with that arrow.
• In the diagram below, the currents i1 and i2 are
  not defined until the arrows are shown.
• Use lowercase variables for current. Uppercase
  subscripts are preferred.

22
Polarities for Voltages

• For voltage, the reference polarity is given by a
  symbol and a symbol, at or near the two
  points involved.
• The actual polarity is indicated by a value that
  is placed between the and - symbols.
• In the diagram below, the voltages v1 and v2 are
  not defined until the and symbols are shown.
• Use lowercase variables for voltage. Uppercase
  subscripts are preferred.

23
Defining Voltages

• For voltage, the reference polarity is given by a
  symbol and a symbol, at or near the two
  points involved.
• The actual polarity is indicated by the sign of
  the value that is placed between the and -
  symbols.
• In the diagram below, the voltages v1 and v2 are
  not defined until the and symbols are shown.

In this case, v1 5V and v2 -5V. These four
labels all mean the same thing.
24
Why bother with reference polarities?

• Students who are new to circuits often question
  whether this is intended just to make something
  easy seem complicated. It is not so using
  reference polarities helps.
• The key is that often the actual polarity of a
  voltage or current is not known until later. We
  want to be able to write expressions that will be
  valid no matter what the actual polarities turn
  out to be.
• To do this, we use reference polarities, and the
  actual polarities come out later.

25
Part 2Energy, Power, and Which Way They Go
26
Overview of this Part

• In this part of the module, we will cover the
  following topics
• Definitions of energy and power
• Sign Conventions for power direction
• Which way do the energy and power go?
• Hydraulic analogy to energy and power, and yet
  another hydraulic analogy

27
Energy
This is the definition found in most
dictionaries, although it is dangerous to use
nontechnical dictionaries to define technical
terms. For example, some dictionaries list force
and power as synonyms for energy, and we will not
do that!

• Energy is the ability or the capacity to do work.
• It is a quantity that can take on many forms,
  among them heat, light, sound, motion of objects
  with mass.

28
Joule Definition

• The unit for energy that we use is the Joule
  J.
• A Joule is a Newton-meter.
• In everything that we do in circuit analysis,
  energy will be conserved.
• One of the key concerns in circuit analysis is
  this Is a device, object, or element absorbing
  energy or delivering energy?

Go back to Overview slide.
29
Power

• Power is the rate of change of the energy, with
  time. It is the rate at which the energy is
  absorbed or delivered.
• Again, a key concern is this Is power being
  absorbed or delivered? We will show a way to
  answer this question.
• Mathematically, power is defined as

Energy, typically in Joules J
Power, typically in Watts W
Time, typically in seconds s
30
Watt Definition

• A Watt is defined as a Joule per second.
• We use a capital W for this unit.
• Light bulbs are rated in W. Thus, a 100W
  light bulb is one that absorbs 100Joules every
  second that it is turned on.

31
Power from Voltage and Current

• Power can be found from the voltage and current,
  as shown below. Note that if voltage is given in
  V, and current in A, power will come out in
  W.

Go back to Overview slide.
32
Sign Conventions or Polarity Conventions

• To determine whether power and energy are
  delivered or absorbed, we will introduce sign
  conventions, or polarity conventions.
• A sign convention is a relationship between
  reference polarities for voltage and current.
• As in all reference polarity issues, you cant
  choose reference polarities wrong. You just have
  to understand what your choice means.

33
Passive Sign Convention Definition

• The passive sign convention is when the reference
  polarity for the current is in the direction of
  the reference voltage drop.
• Another way of saying this is that when the
  reference polarity for the current enters the
  positive terminal for the reference polarity for
  the voltage, we have used the passive sign
  convention.

34
Passive Sign Convention Discussion of the
Definition

• The two circuits below have reference polarities
  which are in the passive sign convention.
• Notice that although they look different, these
  two circuits have the same relationship between
  the polarities of the voltage and current.

35
Active Sign Convention -- Definition

• The active sign convention is when the reference
  polarity for the current is in the direction of
  the reference voltage rise.
• Another way of saying this is that when the
  reference polarity for the current enters the
  negative terminal for the reference polarity for
  the voltage, we have used the active sign
  convention.

36
Active Sign Convention Discussion of the
Definition

• The two circuits below have reference polarities
  which are in the active sign convention.
• Notice that although they look different, these
  two circuits have the same relationship between
  the polarities of the voltage and current.

37
Using Sign Conventions for Power Direction
Subscripts

• We will use the sign conventions that we just
  defined in several ways in circuit analysis. For
  now, lets just concentrate on using it to
  determine whether power is absorbed, or power is
  delivered.
• We might want to write an expression for power
  absorbed by a device, circuit element, or other
  part of a circuit. It is necessary for you to be
  clear about what you are talking about. A good
  way to do this is by using appropriate subscripts.

38
Using Sign Conventions for Power Direction The
Rules

• We will use the sign conventions to determine
  whether power is absorbed, or power is delivered.
• When we use the passive sign convention to assign
  reference polarities, vi gives the power
  absorbed, and vi gives the power delivered.
• When we use the active sign convention to assign
  reference polarities, vi gives the power
  delivered, and vi gives the power absorbed.

39
Using Sign Conventions for Power Direction The
Rules

• We will use the sign conventions to determine
  whether power is absorbed, or power is delivered.
• When we use the passive sign convention to assign
  reference polarities, vi gives the power
  absorbed, and vi gives the power delivered.
• When we use the active sign convention to assign
  reference polarities, vi gives the power
  delivered, and vi gives the power absorbed.

40
Example of Using the Power Direction Table Step
1

• We want an expression for the power absorbed by
  this Sample Circuit.
• Determine which sign convention has been used to
  assign reference polarities for this Sample
  Circuit.

41
Example of Using the Power Direction Table Step
2

• We want an expression for the power absorbed by
  this Sample Circuit.
• Determine which sign convention has been used.
• Next, we find the cell that is of interest to us
  here in the table. It is highlighted in red
  below.

This is the active sign convention.
42
Example of Using the Power Direction Table Step
3

• We want an expression for the power absorbed by
  this Sample Circuit.
• Determine which sign convention has been used.
• Find the cell that is of interest to us here in
  the table. This cell is highlighted in red.
• Thus, we write pABS.BY.CIR -vSiS .

Go back to Overview slide.
This is the active sign convention.
43
Example of Using the Power Direction Table Note
on Notation

• We want an expression for the power absorbed by
  this Sample Circuit.
• Determine which sign convention has been used.
• Find the cell that is of interest to us here in
  the table. This cell is highlighted in red.
• Thus, we write pABS.BY.CIR -vSiS .

Go back to Overview slide.
In your power expressions, always use lowercase
variables for power. Uppercase subscripts are
preferred. Always use a two-part subscript for
all power and energy variables. Indicate whether
abs or del, and by what.
44
Hydraulic Analogy

• The hydraulic analogy here can be used to test
  our rule for finding the direction that power
  goes. Imagine a waterfall. A real waterfall,
  and a schematic waterfall are shown here.

45
Hydraulic Analogy for Power Directions Test

• The hydraulic analogy here can be used to test
  our rule for finding the direction that power
  goes. Imagine a waterfall.

The waterflow is in the direction of the drop in
height. Thus, this is analogous to the passive
sign convention. Thus, if we wrote an expression
for power absorbed, we would write
pABS vi
Since the values are positive, the power absorbed
will be positive. Does this make sense?
46
Hydraulic Analogy for Power Directions Answer

• The power absorbed will be positive. Does this
  make sense?
• Yes, but only if we understand a key assumption.
  In circuits, when we say energy absorbed, we mean
  the energy absorbed from the electrical system,
  and delivered somewhere else.
• In this hydraulic analogy, energy is being lost
  from the water as it falls. This energy is being
  delivered somewhere else, as sound, heat, or in
  other forms. We call this energy absorbed.
  Thus, the power absorbed is positive.

47
Power Directions Assumption 1

• So, a key assumption is that when we say power
  delivered, we mean that there is power taken from
  someplace else, converted and delivered to the
  electrical system. This is the how this approach
  gives us direction.
• For example, in a battery, this power comes from
  chemical power in the battery, and is converted
  to electrical power.
• Remember that energy is conserved, and therefore
  power will be conserved as well.

Positive power delivered by something means that
power from somewhere else enters the electrical
system as electrical power, through that
something. In this diagram, the red power
(nonelectrical) is being changed to the blue
power (electrical).
48
Power Directions Assumption 2

• So, a key assumption is that when we say power
  absorbed, we mean that there is power from the
  electrical system that is converted to
  nonelectrical power. This is the how this
  approach gives us direction.
• For example, in a lightbulb, the electrical power
  is converted to light and heat (nonelectrical
  power).
• Remember that energy is conserved, and therefore
  power will be conserved as well.

Positive power absorbed by something means that
power from the electrical system leaves as
nonelectrical power, through that something. In
this diagram, the blue power (electrical) is
being changed to the red power (nonelectrical).
49
Power Directions Terminology Synonyms

• There are a number of terms that are synonyms for
  power absorbed. We may use
• Power absorbed by
• Power consumed by
• Power delivered to
• Power provided to
• Power supplied to
• Power dissipated by
• There are a number of terms that are synonyms for
  power delivered. We may use
• Power delivered by
• Power provided by
• Power supplied by

50
Another Hydraulic Analogy

• Another useful hydraulic analogy that can be used
  to help us understand this is presented by A.
  Bruce Carlson in his textbook, Circuits,
  published by Brooks/Cole. The diagram, Figure
  1.9, from page 11 of that textbook, is duplicated
  here.

51
Another Hydraulic Analogy Details

• In this analogy, the electrical circuit is shown
  at the left, and the hydraulic analog on the
  right.
• As Carlson puts it, The pump (source) forces
  water flow (current) through pipes (wires) to
  drive the turbine (load). The water pressure
  (potential) is higher at the inlet port of the
  turbine than at the outlet.

Note that the Source is given with reference
polarities in the active convention, and the Load
with reference polarities in the passive
convention. As a result, in this case, since all
quantities are positive, the Source delivers
power, and the Load absorbs power.
52
Another Point on Terminology

• We always need to be careful of our context.
  When we say things like the Source delivers
  power, we implicitly mean the Source delivers
  positive power.

Note that the Source is given with reference
polarities in the active convention, and the Load
with reference polarities in the passive
convention. As a result, in this case, since all
quantities are positive, the Source delivers
power, and the Load absorbs power.
53
Another Point on Terminology

• At the same time, it is also acceptable to write
  expressions such as pabs,source -5000W.
  This is the same thing as saying that the power
  delivered is 5000W.
• However, unless the context is clear, it is
  ambiguous to just write p 5000W. Your answer
  must be clear, because the direction is important!

Note that the Source is given with reference
polarities in the active convention, and the Load
with reference polarities in the passive
convention. As a result, in this case, since all
quantities are positive, the Source delivers
power, and the Load absorbs power.
54
Why bother with Sign Conventions?

• Students who are new to circuits often question
  whether sign conventions are intended just to
  make something easy seem complicated. It is not
  so using sign conventions helps.
• The key is that often the direction that power is
  moving is not known until later. We want to be
  able to write expressions now that will be valid
  no matter what the actual polarities turn out to
  be.
• To do this, we use sign conventions, and the
  actual directions come out later when we plug
  values in.

Go back to Overview slide.